Average Error: 3.7 → 0.6
Time: 4.8s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.9800446771093483 \cdot 10^{217}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 7.947264576269877 \cdot 10^{204}:\\ \;\;\;\;\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \end{array}\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.9800446771093483 \cdot 10^{217}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 7.947264576269877 \cdot 10^{204}:\\
\;\;\;\;\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + 27 \cdot \left(a \cdot b\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r748269 = x;
        double r748270 = 2.0;
        double r748271 = r748269 * r748270;
        double r748272 = y;
        double r748273 = 9.0;
        double r748274 = r748272 * r748273;
        double r748275 = z;
        double r748276 = r748274 * r748275;
        double r748277 = t;
        double r748278 = r748276 * r748277;
        double r748279 = r748271 - r748278;
        double r748280 = a;
        double r748281 = 27.0;
        double r748282 = r748280 * r748281;
        double r748283 = b;
        double r748284 = r748282 * r748283;
        double r748285 = r748279 + r748284;
        return r748285;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r748286 = y;
        double r748287 = 9.0;
        double r748288 = r748286 * r748287;
        double r748289 = z;
        double r748290 = r748288 * r748289;
        double r748291 = -8.980044677109348e+217;
        bool r748292 = r748290 <= r748291;
        double r748293 = x;
        double r748294 = 2.0;
        double r748295 = r748293 * r748294;
        double r748296 = t;
        double r748297 = r748289 * r748296;
        double r748298 = r748288 * r748297;
        double r748299 = r748295 - r748298;
        double r748300 = a;
        double r748301 = 27.0;
        double r748302 = b;
        double r748303 = r748301 * r748302;
        double r748304 = r748300 * r748303;
        double r748305 = r748299 + r748304;
        double r748306 = 7.947264576269877e+204;
        bool r748307 = r748290 <= r748306;
        double r748308 = r748294 * r748293;
        double r748309 = r748289 * r748286;
        double r748310 = r748296 * r748309;
        double r748311 = r748287 * r748310;
        double r748312 = r748308 - r748311;
        double r748313 = r748300 * r748301;
        double r748314 = r748313 * r748302;
        double r748315 = r748312 + r748314;
        double r748316 = r748300 * r748302;
        double r748317 = r748301 * r748316;
        double r748318 = r748299 + r748317;
        double r748319 = r748307 ? r748315 : r748318;
        double r748320 = r748292 ? r748305 : r748319;
        return r748320;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target2.7
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -8.980044677109348e+217

    1. Initial program 29.8

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*1.3

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]
    4. Using strategy rm

    5. Applied associate-*l*1.2

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)}\]

    if -8.980044677109348e+217 < (* (* y 9.0) z) < 7.947264576269877e+204

    1. Initial program 0.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*3.8

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Taylor expanded around inf 0.5

      \[\leadsto \color{blue}{\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)} + \left(a \cdot 27\right) \cdot b\]

    if 7.947264576269877e+204 < (* (* y 9.0) z)

    1. Initial program 26.8

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*0.9

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Taylor expanded around 0 0.9

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.9800446771093483 \cdot 10^{217}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 7.947264576269877 \cdot 10^{204}:\\ \;\;\;\;\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))